Projectile



Dec. 30, 1924.

L. B. TAYLOR PROJEGTILE Filed Aug. 24, 1921 5 Sheets-Sheet l De'c. 30, 1.924. 1521406 y l.. B. TAYLOR y PROJECTILE Filed Aug. 24, 1921 5 Sheets-Sheet 2 y @www Dec. 30, 1924. 1,521,406

y L.. B. TAYLOR PROJECTILE iled Aug. 24, 1921 5 sheets-sheet a SFTS tetes PROJECTLE.

Application led August 24, l92.

To all @07mm t may conce/Mi.'

Be it known that l, linsLin BowN TAY- Lca, a subject of the ling ot' Great Britain, residing at Grange Road, Bournbrooli, Birmingham, in the county of llarwick, England, have invented certain new and useiul improvements in or Relating to lrojectiles, ot which the following is a specification.

rlhe said invention relates to the construction ot projectiles tor ordnance and small arms and in order that the said invention may be the better understood l remarir that heretofore in the construction oi such bodies the location of the centre of inertia or centroid in relation to the length ol' anis and radius oi gyration o-t' the body has been more or less left to chance or arbitrarily fixed with the result that the kinetic energy developed by a given impulse has not been conserved but on the contrary has been dissipated owing to premature and exaggerated precessional disturbances induce-d by or resulting from and varying with the amount of error in the location ot the centroid having regard to the length ot axis and radius ot gyration of the body.

The object oi the said invention is to eliminate wholly or in great part precessional aberrations in proyectiles due to the cause hereinbeiore referred to and further to establish a norm or standard by the application oil which to the construction of such bodies there results an optimum of eiilciency due to the elimination wholly or in great part oi' the said precessional aberrations. 1

The underlying principles of my invention and their practical application to proliectileconstruction as hereinafter fully described with reference to the acompanying drawings have been determined byvexperinient and a consideration oi the following` mathematical propositions involved.,a namely i. Maximum gyroscopic stability or equilibriun exists in a rotating rigid body when the axis of rotation is without precession.

2. Jhe precession induced or developed in a rotating rigid body by a force acting to turn the axis at an angle to its normal or initial plane of rotation will be directed at Serial No. 494,840.

an angle tothe said plane Whose versed sine is commensurate to the force applied, and will readily come under control in proportion as this versed sine is small. y

Proposition l is axiomatic and proposition 2 will be evident from a consideration of the diagrams Figures l and 2 of the drawings. Y

Fig. l is a diagrannnatic view illustrative or the lirst of the above propositions.

Fig. 2 is a diagrammatic view illustrative ot' the second ot the above propositions.

Fig. 3 is a diagrammatic view applying the principle of my invention to a shell and illustrating the cone of restitution and the radins of restitution relative thereto.

Figs. l and 5 illustrate diagrammatically two project-iles, the cylindrical portions of which are identical and the mass equal but having diierent noses.

Fig. 6 illustrates diagrammatically one iform of shell having a hollow nose or cap applied thereto and shows the concavity in the cylindrical portion to compensate for the weight ot the nose or cap.

Fig. 7 is a somewhat different construction showing diagrammatically the assembling of the cap or nose, upon the cylindrical portion ot the shell by means of a ring.

Fig. 8 shows riiling ridges adapted to cooperate with corresponding riding grooves of a shell.

Dealing with the iirst part of this proposition and referring to Figure l, A represents a rotating rigid body the normal or initial axis of rotation ot which is denoted by the letters m, gj.

01. g/l denotes the plane of the said axis due to precession induced lby a torce of say m lbs. and :U23 1/2 the plane oit the said axis due to precession induced by a force of say n lbs.

Let o 'denote the point of intersection of the precessing axes m1, gz/l and m2, y2 with the normal airis y/ and with the centre C* and radius equal to airis o7 y/ describe the are a, o cutting 111, 1/1 and m2, y2 at 7/1 and y2 respectively and thus lining the eX- tremities of the said axes.

By now dropping the lines y1 ya and y2 g/ from the points 571 and y2 respectively and perpendicular to te, y an'd joining the points ya and yt at rwhich they intersect ther-arc a, Z) to the point We completefiguros (sections on ythe vertical axes) 'of they ln the said diagram the body outlined iny heavy lines may represent a top or more yappropriately to the subject matter et the present specilication a ymissiler gyrating on its point or nose.

yGr is the centre or mass or' inertia; l), l the piane of gyration; A, B the axis o't' gyration and 7) is the point or nose of the body or missile when the saine has a short taper or conical iront end. 1 is the point or nose of the said body when the saine has a taper or conical i'ront part or end (indicated in heavy dotted lines in the diagram) the axis of which is three times that of' the short cone justy referred to. ,y

It ce, fc represents the plane on which the point b is contacting when the body is rotating With its axis normal to the said plane rc, thatis to say, when there is no rprecessional aberration in the body, and :01, al denote the plane of the circle of preces* sion when, under the effect of precessional aberration the axis occupies the inclined position indicated by the dotted lines b2, bg 52, "if then the distance between the said planes ai, a; and zal, .r1 denoted by the letter 0 in the diagram, measures the vertical displacement of the centre ot gravity G, due to precessioii, and the product o the said distance 0 into the mass or Weight M of the body is the measure o the Work which would have to be performed to restore the body to its normal or ertical condition.

New taking the body having the same cylindrical portion as the iirst body, but with the conical front end represented in heavy dotted lines, the axis of the said conical part being as before stated three times the length ot the airis of the conical'part of the iirst considered body. This second body is presumed to be the same weight or mass M as the first body and by construction its centre ot gravity is maintained at the point G.

Let y, 1,1 represent the plane ivithwhich the point b1 is contacting When the body is rotating normally and g/l, g/l the plane of the circle of precession of the point b1 Which circle is taken for comparative argument as equal to the circle of precessi'on of the point Zi of the first considered body then tliefdistance between the planes y, 1/ and e/l, i/l indicated by 0.1 in the diagram, measures the vertical' displacement ot the centre oi inertia G in this second case and the product ot the distance o1 into M, the mass or Weight of the body is, as before, the measure et the work which would require to be performed to restore this body toits normal or vertical position.

rEhe distances o and 01 are the versed si'nes of the respective angles of precession and qi and are in flact comparable With d, y yand c, y respectively in the first diagram of re'l erence Figure 1 therefore the second part of proposition 2 is demonstrated.

Further from the above I deduce the corollary that the products MC) and MXGl rare measures of ther energy dissipated owing to precessional aberration when the distance f ot the centre G to the point has the respective lengths G o and G 1 the circle oi procession rot the points Y), b1 being in each case equal.

To illustrate the manner in which l apply the above mathematical principles to provide a standard or norm for use in projectile constructionand alsoy to define ceis tain terms of reference, l have represented in Figure 3 a. longitudinal section through the ot' a bullet having a cylindrical rearr part and hollow conical '.tront part or nose: A B C l? being the section of the cylinydrical part and C l) o beine` the outline ot the outer surface of the hollowv conical cap oi' nose.

721 is the anis oif the bullet and G is the centr-e of the rectangular middle plane or section ot the cylindrical part. (il and 7) denote the centi-es ot inert-ia or points at Awhich the n. s may be deemed to be concentrated ou either side of the afgis l. 7N when the projectile is rotating about the said axis: Ga? and G52 being therefore radii of 'ation denoted `tor convenience oi re'lerence hereafter by the symbol R2 in the said Figure 3. The points 0f and b2 in the practical. construction ot a missile are determined as hereinafter described and to the dimension a? b2 that is QRZ I hereinafter apply the term dynamic calibre.

By joining` {l} and Zig to the extremity 7; ot the axis Z2, o1 l obtain the dotted conical figure al, Y), 712.

VTo' this conical ligure l propose to apply the terni cone ot restitution77 and 'to the axis G 7) ot the said cone denoted in the said Figure 3 by the symbol lil the terni radius oif restitution.

l To the ratio to length of ogival head in projectile structure.

The radii R1 and R2 enable me to arriveat the angle of cone of restitution whose versed sine must remain infinitesimal if I am to preserve an optimum'of moment-um in the projectile.

In the diagram Figure 3 I have represented the cylindrical portion of the projectile, the diameter of which is detein'iined by the calibre, as equal in length to two dynamic calibres which length I deem as th results of my experiments the preferable length of the said cylindrical part.

The points al and b2 which determine the dynamic calibre are ascertained as follows: I take a cylinder of the requisite material, calibre and weight of the complete projectile to be constructed and by well-established mathematical rules and calculations lind the centres of inertia for the same when rotating about its axis.

These points determine, the dimension of the base of the cone of restitution or factor QRQ of the formula which I have defined as the dynamic ratio.

I maintain the centre of gravity of the missile at the centre of ligure of the cylindrical part A, B, C, D, that is to say, I deli` nitely locate the plane of gyration of the mass at the middle cross sectional plane of the said cylindrical part.

The base of the cone of restitution is thus fixed and also one extremity of the radius of restitution or factor R1. In order to maintain the centre of gravity G of the mass of the complete projectile at the centre of the cylindrical part of the projectile when the hollow conical cap or nose is ap plied to the front end of the said cylindrical part I hollow out the said front end as illustrated by Fig. 5 to an extent proper to compensate for the weight of the said cap or nose.

Cr I may partially compensate the weight of the conical iap or nose by giving a convex or curved form to the base of the projectile as shown in Figure 8 the additional weight thus added to the base half of the cylindrical part proportionately reducing the extent to which the front or nose end of the said cylindrical part is hollowed out. 'Ihe radius of curvature of J"he base may be struck from the point of the bullet but in the case of a sabot carrying shell the radius of curvature` is preferably struck from the centre of gravity of the bullet.

In Figures 4 and 5 I give examples of two projectiles, shown in outline, the cylindrical por ions of which are identical and the mass assumed to be equal.

Figure i has a radius of restitution equal to three dynamic calibres and Figure 5 a radius of restitution equal to tive dynamic calibres. The cones of ,restitution in the said gurcs are indicated by heavy dotted lines and in tine dotted lines I have indicated the outlines' of the cones generated by the radii of restitution of the respective missiles assuming for the purpose of comparison that the diameters of the circles of precession of the respective noses of the missiles are equal to the dynamic ratio which is the same in each case. Therefore the versed sines ofthe angles of the cones of restitution will respectively have the same pr0 portion to each other as the versed sines of the angle of the respective cones of precession and this ratio or proportion would be maintained whatever the angle of precession of the missiles.

It has already been demonstrated with reference to Figures l and 2 that the smaller the versed sine of the angle of precession to the axes of rotation the more readily will the precession come under control and also the less will be the dissipation of the gyroscopic energy of the body.

It therefore follows that the missile F igure 5 has superior gyroscopic momentum and stability to the missile of Figure l the superiority arising from the increased length of the radius of restitution R1 which gives a higher value to the dynamic ratio The cones of restitution constitute figures of merit or graphical representations indicative of the gyro-stability of the missiles, and a further advantage which attends the obtaining of the said cones of restitution is that the inclination of the sides of the said cones provides me with the most desirable angle or pitch for the rifling of the barrels of fire-arms to be constructed for the discharge of the said projectiles. I have found that where the said angle or pitch is made equal to the angle of restitution the ranging power or ability of the missile to maintain the nose on7 direction from the muzzle to the target, is a maximum when the riling has a length equal to one half turn or at most to a complete turn. The rifling is formed at the muzzle end or preferably at the breech end of the barrel and the interior of the barrel beyond the riting is left with a smooth bore.

By assigning a predetermined value to the dynamic ratio ballistic properties will be obtained.

In column l of the following table, headed Table of comparative values, we assign llO predetermined values to the axial length of the cone of restitution or dynamic ratio Ri 2K2 TaZiZe of comparative talues.

Dynamic ratio. angle of Verscd sine Cosine X cone of X100 (index 100 (index i restitution of percentof percent- 2K2 (also preage 0i' age of [erred pitch energy energy of riiing). dissipated) available).

Dryrfcs.

2 34 l). S() U0. 20 18. 28 13 94. 87 14. 2 2. 98 97. 02 11.19 1.85 95.15 Si. 28 1. 36 9S. (il 8. S 1.00 99. 7. 8 0. 77 99. 23 5. 2l 0. (i1 99. 39 5. 43 0. 50 99. 50 5. 13 O. 41 .99. 59 4. 46 O. 35 99. G5 4. 24 0. 29 99. 71 4. 0. 25 99. 75 49 0. 22 99. 78 3. O. 2O 99. 80 3. 22 0. 17 99. 83 3. 11 0. 15 99. 85 3. 0 0. 14 Q9. 86 2. 52 0. 13 99. S7

A reference to column 2 of the above table shows at a glance the preferred angle of pitch of the riiiing for a. projectile When its dynamic ratio has been determined and reference to columns 3 and Ll gives the percentage of energy which Will be dissipated and the percentage of the terminal or available energy, the one being complementary of the other.

lt will be noted that the original shape of the front end or cap of the missiles represented in no Way afl'ects the factors governing the method of construction hereinbefore described and the properties conferred thereby on the missile and l Wish it to be understood that the said front end or cap may be otherwise shaped than truly conical, for eX- ample, the said cap or front part may have what is technically termed an ogival shape.

Preferably the said front end or cap is connected to the rear or cylindrical partv of the projectile by a screwed ring as is illustrated in F ig. 7, which ring may constitute the driving or steadying band or one of the driving or steadying bands of `:he projectile, and the cylindrical part of the projectile may be and preferably is provided racines on its exterior surface by casting or otherwise with a series of ribs or feathers shown diagrammatically in Fig. 8 and marked e, the said ribs or feathers having an inclination to the plane of the axis equal to the inclination of the sides of the cone restitution and angle of the pitch of the rifling or in other Words the said ribs or feathers fit into the rifling grooves of the barrel when the said grooves have the preferred inclina.- tion.

By the improvements hereinbefore described l have found that a projectile when tired from a small arni or piece of ordnance receives and conserves an optimum of 0yrostatic momentum and maintains througl iut its flight its angle of departure, thereby avoiding the destructive precessional aberrations which obtain in an ordinary projectile due to constant change of the axis of gyration from that at Which it left the muzzle of the tire-arm. By reason of the planing phenomenon asserting itself throughout the descending portion of the trajectory the projectile Will strike the'ground on the edge of its base its axis preserving the same or approximately the same direction as that which it had when it left the lire-arm.

l claim-- 1. A bullet or projectile having a cylindrical portion and so constructed thatY .its plane of gyration is preserved at the axial center of the cylindrical portion of the said projectile and having a cone of restitution, the axis of which is equal to at least three dynamic calibres, of the projectile.

2. A bullet or projectile having a cylindrical and a tapered portion, said cylindrical portion having a length equal or approximately equal to two dynamic calibres and in which the centre of mass or centroid of the projectile is preserved at the axial centre of the said cylindrical part.

3. A bullet or projectile having a cylindrical and a tapered portion, said cylindrical portion having a length equal or approximately equal to two dynamic calibres and in which the centre of mass or centroid of the projectile is preserved at the. axial centre of the said cylindrical part by hollowing out the said cylindrical part at the end to which the nose is applied, the portion of the axis of the bullet or projectile from the middle of the cylindrical part to the tip of the tapered portion having a. length equal to at least three times the dynamic calibre of the missile.

In testimony whereof I have hereunto set my hand. l

LESLIE B01/VN TAYLUR. 

